In Lesson 1 - available free here - of my course on advanced analytical techniques applied to sports betting, we talk about “the hidden generator” as a mental model for understanding the complexities of real-world outcomes of sporting events. You see, there is something unique about sports betting compared to most other forms of gambling: we don’t know the rules. “Of course we know the rules,” you say, smacking me over the head with a copy of the NFL rulebook. But I’m not talking about the rules of football, I’m talking about the rules of probability.
If you roll two dice, the probability of rolling a seven is 1/6. So, you step up to the craps table, throw a chip down on the pass line, and roll a seven. Winner! Next roll, you do it again. Seven. Winner! Before you roll a third time, you ask yourself “what is the probability of rolling another seven?” The answer is 1/6. The results of the first two rolls are completely useless when evaluating the third roll, because before the first roll we already knew everything there is to know about how dice work. We haven’t learned any new information from the first two rolls.
The Minnesota Vikings were 2-point favorites at home against the Green Bay Packers in Week 1. The Vikings crushed the Packers 23-7. Suppose the Packers played in Minnesota again in Week 2 – what would the line be? Our dice-rolling example would suggest it should be Vikings -2 again… but should it? The probabilities for dice rolling are governed by rules of geometry and physics that have been fully understood for centuries. The probabilities for football are governed by no such natural laws – they are estimated by the collective wisdom of markets, taking into account a ton of complex information about the players, coaches, conditions, etc. As the information changes, the estimates can change as well. We didn’t know a week ago that the Vikings would win by 16. We know now that they did, and the market has learned new information. The big question is, how much has it learned? Learning nothing and lining this hypothetical rematch at Minnesota -2 would be pretty obviously wrong. Learning so much that it forgets everything else it knew and lining the rematch at Min -16 would also be obviously wrong, because markets don’t usually miss by that much – a 2-point favorite winning by 16 would presumably have benefited from at least some random good luck that is unlikely to repeat in the next game. So that leaves the space in between Minnesota -2 and Minnesota -16 for us to work with.
Taking prior probability assessments and updating them with new information is squarely in the domain of Bayesian Analysis, one of my favorite things in the whole world. Bayesian Analysis has a lot of complicated math behind it, but we’re not going to go into that at all here. We’re going to look at the Bayesian approach not as a set of calculations, but as a way of thinking. Because if you take the complicated math and boil it down to its essence, you get something that I’m calling “the fundamental equation of learning”:
What actually happened – what we expected to happen
=
What we learned + Random noise
Or, even more simply,
Surprise = Signal + Noise
The Vikings performed 14 points better than the market expected, and the Packers performed 14 points worse than the market expected. This is the “surprise” that we need to split out between “signal” and “noise.” What if the Vikings had won by two instead of by 16? Then there would have been no surprise – the market expected exactly what happened, and a run back of the Minnesota -2 spread would be perfectly reasonable if these teams were to play again.
Alright, that’s great, so far we’ve said a lot of words to justify anything between Vikings -2.5 and Vikings -15.5 for a game that is not even being played. Get to the point, Matt! So, there are two big questions that will help us separate the surprise into signal and noise:
1) What degree of certainty was in the initial prediction?
The market drew a line in the sand, and that line was “the Vikings at home are two points better than the Packers on the road.” What we can’t tell is the market’s level of certainty in that assessment. You can get a 2-point spread between two teams full of experienced, established players and coaches such that we know exactly what we’re dealing with. You can also get a 2-point spread between teams of no-names in a league that’s never played a game before today. They’re both 2-point spreads, but with different degrees of certainty.
The more certainty there is in the initial prediction, the more likely it is that any surprise is due to noise, not signal.
This is why the first two dice rolls didn’t change our assessment of the third: the initial prediction of a 1/6 probability of rolling a seven had FULL certainty.
A Week 1 line will usually have less certainty than a Week 17 line, because this is the first time that these groups of players and coaches have performed together. There might be more certainty from “we know at this point how good Aaron Rodgers and Kirk Cousins are,” but also less certainty from “we don’t know how much Rodgers’ ability will deteriorate with an additional year of age.”
2) How much randomness does the process have?
This has less to do with the individual teams and more to do with the sport itself. Sports are so entertaining because they contain a mixture of skill and luck, of predictability and unpredictability. Would you watch a game where one team was guaranteed to win? Would you watch televised roulette where the outcome was completely random with no substance at all? Likely not. (Although I am old enough to remember televised blackjack tournaments near the end of the poker boom).
The more randomness there is in the game, the more likely it is that any surprise is due to noise, not signal.
The real question here is: How likely is it that a 2-point favorite wins by 16? This can be answered easily enough using alt spreads.
There’s a little bit of reverse engineering going on here: the rarer it is for a 2-point favorite to win by 16, the more unlikely it is that the Vikings should have been a 2-point favorite in the first place.
Now let’s break down the Week 2 board through this lens of surprise, signal, and noise:
Chargers @ Chiefs
LAC Week 1: -3.5, won by 5 (+1.5 point surprise)
KC Week 1: -6, won by 23 (+17 point surprise)
Net surprise: 15.5 for KC
Pre-Week 1 lookahead: KC -3
Week 2 line: KC -3.5
Implied signal: 0.5 for KC
For the sake of simplicity, I’m making the admittedly stupid assumption here that all points are equal. (If you’re trying this at home, moneylines on a logit scale would be a more accurate choice.) So, saying that the market moved only 0.5 points toward KC on 15.5 points of surprise would be a bit of a mischaracterization, because 3 to 3.5 is the most important half-point there is.
Still, the Chiefs game was 37-7 before garbage time and there were some questions starting to creep in about Mahomes’ effectiveness that were soundly put to rest in Week 1. I’d say this is an underreaction and to take the Chiefs, but there are some injury concerns with Mahomes that might be driving the market at this point.
Colts @ Jaguars
IND Week 1: -7, tied (-7 point surprise)
JAX Week 1: +3, lost by 6 (-3 point surprise)
Net surprise: 4 for JAX
Pre-Week 1 lookahead: IND -4.5
Week 2 line: IND -4
Implied signal: 0.5 for JAX
Commanders @ Lions
WSH Week 1: -3, won by 6 (+3 point surprise)
DET Week 1: +6, lost by 3 (+3 point surprise)
Net surprise: 0
Pre-Week 1 lookahead: WSH -1
Week 2 line: DET -2
Implied signal: 3 for DET
Again, it’s inaccurate to call +1 to -2 a “3-point move.” Still, it seems the market liked what it saw from the Lions, who were surprisingly competitive with the Eagles, a little bit more than what it saw from the Commanders, who barely escaped with a win against the Jaguars.
Dolphins @ Ravens
MIA Week 1: -3, won by 13 (+10 point surprise)
BAL Week 1: -6.5, won by 15 (+8.5 point surprise)
Net surprise: 1.5 for MIA
Pre-Week 1 lookahead: BAL -4
Week 2 line: BAL -3.5
Implied signal: 0.5 for MIA
Jets @ Browns
NYJ Week 1: +6.5, lost by 15 (-8.5 point surprise)
CLE Week 1: +2, won by 2 (+4 point surprise)
Net surprise: 12.5 for CLE
Pre-Week 1 lookahead: CLE -5.5
Week 2 line: CLE -6
Implied signal: 0.5 for CLE
Week 2 is known as overreaction week, but it’s not living up to that name so far. This feels like an underreaction. I’m on the Browns.
Buccaneers @ Saints
TB week 1: -2.5, won by 16 (+13.5 point surprise)
NO week 1: -6, won by 1 (-5 point surprise)
Net surprise: 18.5 for TB
Pre-Week 1 lookahead: TB -3
Week 2 line: TB -3
Implied signal: 0
This one is even more puzzling than the last one. I don’t understand how anyone could think a fair line was -3, then watch last week’s games and say a fair line is still -3. I guess it’s possible the market is discounting the Bucs’ big win because of the Dak Prescott injury and the fact that they only scored 19 points. But there’s a difference between discounting and not counting at all. I like the Bucs in this one.
Panthers @ Giants
CAR Week 1: -2, lost by 2 (-4 point surprise)
NYG Week 1: +5.5, won by 1 (+6.5 point surprise)
Net surprise: 10.5 for NYG
Pre-Week 1 lookahead: NYG -1
Week 2 line: NYG -2.5
Implied signal: 1.5 for NYG
Seahawks @ 49ers
SEA Week 1: +6, won by 1 (+7 point surprise)
SF Week 1: -6, lost by 9 (-15 point surprise)
Net surprise: 22 for SEA
Pre-Week 1 lookahead: SF -8.5
Week 2 line: SF -9
Implied signal: 0.5 for SF
There are even some 9.5s out there. The only explanation I can come up with is George Kittle returning from injury. Still, we’ve gone from overreaction, to underreaction, to “Buckingham Palace Guard” levels of no reaction. Give me the points please.
Falcons @ Rams
ATL Week 1: +6, lost by 1 (+5 point surprise)
LAR: +2, lost by 21 (-19 point surprise)
Net surprise: 24 for ATL
Pre-Week 1 lookahead: LAR -12
Week 2 line: LAR -10.5
Implied signal: 1.5 for ATL
This also seems like a bit of an underreaction given how many unknowns were on this Falcons team heading into Week 1.
Cardinals @ Raiders
ARI Week 1: +6, lost by 23 (-17 point surprise)
LV Week 1: +3.5, lost by 5 (-1.5 point surprise)
Net surprise: 15.5 for LV
Pre-Week 1 lookahead: LV -2.5
Week 2 line: LV -6
Implied signal: 3.5 for LV
This seems like an overreaction, especially with the possible return of JJ Watt. Give me the Cards and the points.
Texans @ Broncos
HOU Week 1: +7, tied (+7 point surprise)
DEN Week 1: -6, lost by 1 (-7 point surprise)
Net surprise: 14 for HOU
Pre-Week 1 lookahead: DEN -10.5
Week 2 line: DEN -10
Implied signal: 0.5 for HOU
When you ask yourself “what was the degree of certainty in the initial prediction?”, a new quarterback and a first-time head coach are two things that would push that certainty down. Russell Wilson looked OK, but the way Nathaniel Hackett botched the end of the game does not inspire a lot of confidence in his ability to perform as a competent NFL head coach…not to mention facing widespread national ridicule and then having to go back out there against another bad team for his second career game. Texans and the points, please.
Bears @ Packers
CHI Week 1: +6, won by 9 (+15 point surprise)
GB Week 1: +2, lost by 16 (-14 point surprise)
Net surprise: 29 for CHI
Pre-Week 1 lookahead: GB -9.5
Week 2 line: GB -10
Implied signal: 0.5 for GB
I’m not going to pretend I have an explanation for this one. I don’t.
Titans @ Bills
TEN Week 1: -5.5, lost by 1 (-6.5 point surprise)
BUF Week 1: -2, won by 21 (+19 point surprise)
Net surprise: 25.5 for BUF
Pre-Week 1 lookahead: BUF -8.5
Week 2 line: BUF -10
Implied signal: 1.5 for BUF
Vikings @ Eagles
MIN Week 1: -2, won by 16 (+14 point surprise)
PHI Week 1: -6, won by 3 (-3 point surprise)
Net surprise: 17 for MIN
Pre-Week 1 lookahead: PHI -2.5
Week 2 line: PHI -1.5
Implied signal: 1 for MIN
Patriots @ Steelers, Bengals @ Cowboys
These two games fall under “Not Applicable” in this framework. Injuries to TJ Watt and Dak Prescott caused these lines to move not necessarily as a reaction to what we learned about these teams in Week 1, but because the teams themselves have significantly changed.
All in all, it’s been an underwhelming “overreaction week” so far with ARI/LV the only game where it looks like the markets are overreacting to what happened in Week 1. In fact, I would argue the markets are actually underreacting on some of these teams.
Best of luck in Week 2!